Two-orbital Hubbard model vs spin $S=1$ Heisenberg model: studies on clusters

Abstract

We perform exact numeric calculations for the two-orbital Hubbard model on the four-site cluster. In the limit of large on-site coupling the model becomes equivalent to the spin $S=1$ Heisenberg model. By comparing energy spectra of these two models, we quantified the range of interaction parameters for which the Heisenberg model satisfactorily reproduces the two-orbital Hubbard model. Then we examined how the spectrum evolves when we are outside of this region, focusing especially on checking of how it is modified when various ways of interatomic hoppings of electrons between different orbitals are taken into account. We finally show how these modifications affect the dependence of specific heat on temperature.Comment: 8 pages, 7 figures, 2 table